For grilling, slicing, and putting on a roll, I think Flank Steak might be a good choice. For the "other" type of steak sandwich (i.e. Philly Cheese Steak), I'll slice just about any cut of steak really thin, throw it in a hot skillet with some thin-sliced onions, season w/ Lowery's and quickly cook until the onions are soft, melt a slice of provolone on top, then use to fill a nice roll.

My usual go-to for sandwiches or soft tacos and such is flank steak, but grilled flat iron is my favorite these days - usually a bit less expensive than flank, really rich, beefy flavor that stands up to horseradish sauce, salsa verde and other salsas...very satisfying.

I live in a small town, and the butcher doesn't do cuts like flat iron, skirt, or if he does he calls them something else. And for some reason he prices flank steak really high. But he sells a tri tip steak very reasonably, I grilled it first over high heat on both sides to sear and then moved it to a lower heat part of the grill for several more minutes per side. It was fantastic.

If you have a professional slicer, you can slice the steak so thin that you can actually use a "better" (i.e. more expensive) cut of meat. I often do this for parties and serve on the mini buns "sliders" with a horseradish cream or blue cheese fondue and people are so impressed...but a little of that goes a long way.

Beef Roasts are always a good staple to have on hand for quick meals, leftovers and sandwiches. Cook it in a slow cooker or low at 325 in the oven with some cooking liquid, spices and onions if you like. Slice it thin when done, freeze slices for later, or use now to make roast beef sandwiches. Serve cold or hot.

Cube steaks . . . these are cuts from rounds or chucks that are hand cut thin and run trough a macerator machine that takes a tougher cut into a more tender steak. This type of steak was very popular when I was a child, then died off. It is now making a come back in the US. I am seeing in many stores now. Prefect for steak sandwiches and very cheap, though beef in general is high at the moment.

One kitchen gadget I find myself using more and more for all cheaper cuts of meat is a needle (jaccard) tenderizer. A little spring loaded thingy with multiple very sharp blades. (something to consider if you have small kids in the house as it can bite). I find it does a great job on tougher cuts of meats..and to make 'cube steak/country fried steak' Or even use chuck and tenderize them for kabobs. Tri-Tips..etc.
I found mine at 'Academy Sports" in the grilling section...and have seen them in supermarkets.